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Analytic multifunctions, the \({\bar\partial}\)-equation, and a proof of the Corona theorem. (English) Zbl 0602.32002
The purpose of this article is to give some application of a recent theorem by Alexander-Wermer and Slodkowski on the structure of certain polynomial hulls. The authors prove that this theorem gives a useful method of constructing analytic functions with prescribed properties in the disc. In particular it yields a rather easy proof of the Corona problem for two generators, and also implies Wolf’s theorem on the \({\bar \partial}\)-equation.
Reviewer: S.F.Krendelev

MSC:
32A30 Other generalizations of function theory of one complex variable
30G30 Other generalizations of analytic functions (including abstract-valued functions)
32E20 Polynomial convexity, rational convexity, meromorphic convexity in several complex variables
35N15 \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs
32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
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